Leeds boss Marcelo Bielsa admitted Crewe made life difficult for his side before three late goals secured a 3-0 Carabao Cup win at a sold-out Elland Road.
Kalvin Phillips finally broke Crewe's stubborn resistance deep in the second half before Jack Harrison sealed Leeds' passage to the third round with two more in the last five minutes.
Bielsa's side spurned a hatful of chances after they had shifted through the gears, but Sky Bet League One side Crewe refused to roll over, holding firm until the 79th minute.
Bielsa said: "We took a very long time to score and missed a lot of chances. It was a very contested game. Even if they did not create a lot they disputed every ball.
"The initial formation they started with took us the start of the game to accommodate to it. In both halves we missed 10 chances."
Bielsa made six changes from the side which started in Saturday's 2-2 Premier League draw against Everton.
Adam Forshaw made his first senior appearance in almost two years, Diego Llorente returned after injury and club record signing Rodrigo was also among the starters.
"Every player that played did so justifying why," Bielsa said. "Some because they had played less in pre-season, some others coming back from injury.
"Some because they had the level of a starter but play less minutes. Some of them because they can play more than once a week. We pick the players with each case in mind."
Two-goal Harrison maintained his impressive start to the season and Bielsa added: "He unbalanced a lot through his sector.
"He linked up well with Junior (Firpo). He, and Junior as his team-mate, they generated a lot."
Crewe boss Dave Artell revealed Bielsa had paid him and his side a big compliment.
"Marcelo Bielsa said at the end that we set up magnificently because they didn't know what we were doing for the first 20 minutes and it was a difficult one to work out," Artell said.
"So I'm hoping that's a compliment. I do feel we made a good fist of it.
"I think the fact that the likes of Patrick Bamford ended up on the pitch and the team Marcelo chose reflected the fact we set up really well.
"It took to the 79th minute and a set-piece, which is so, so disappointing from our point of view."
Artell was delighted his players did not freeze in front of a crowd of 34,154 and said his club's fans also played their part.
"You can see why this historic football club and their fans are held in such high regard up and down the country. It was a magnificent atmosphere," he added.
"If you can't get the best out of yourself in a stadium full to capacity like this, you've got to do something about it and our players certainly weren't daunted."
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